Related papers: Meaning of Interior Tomography
Intrinsic imaging or intrinsic image decomposition has traditionally been described as the problem of decomposing an image into two layers: a reflectance, the albedo invariant color of the material; and a shading, produced by the…
Intrinsic core generalises the finite-dimensional notion of the relative interior to arbitrary (real) vector spaces. Our main goal is to provide a self-contained overview of the key results pertaining to the intrinsic core and to elucidate…
We present a general theory of optical coherence tomography (OCT), which synthesizes the fundamental concepts and implementations of OCT under a common 3D k-space framework. At the heart of this analysis is the Fourier diffraction theorem,…
Tomograms, a generalization of the Radon transform to arbitrary pairs of non-commuting operators, are positive bilinear transforms with a rigorous probabilistic interpretation which provide a full characterization of the signal and are…
Medical imaging is an invaluable resource in medicine as it enables to peer inside the human body and provides scientists and physicians with a wealth of information indispensable for understanding, modelling, diagnosis, and treatment of…
We describe and examine an algorithm for tomographic image reconstruction where prior knowledge about the solution is available in the form of training images. We first construct a nonnegative dictionary based on prototype elements from the…
{\em Quantum Fourier analysis} is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum…
Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a…
The Fourier inversion of phased coherent diffraction patterns offers images without the resolution and depth-of-focus limitations of lens-based tomographic systems. We report on our recent experimental images inverted using recent…
The present short review article illustrates the latest theoretical developments on quantum tomography, regarding general optimization methods for both data-processing and setup. The basic theoretical tool is the informationally complete…
A basic problem in machine learning is to find a mapping $f$ from a low dimensional latent space $\mathcal{Y}$ to a high dimensional observation space $\mathcal{X}$. Modern tools such as deep neural networks are capable to represent general…
A sample of some relevant developments that have taken place during the last twenty years in classical and quantum tomography are displayed. We will present a general conceptual framework that provides a simple unifying mathematical picture…
Blur is an image degradation that is difficult to remove. Invariants with respect to blur offer an alternative way of a~description and recognition of blurred images without any deblurring. In this paper, we present an original unified…
Tomography has made a revolutionary impact on diverse fields, ranging from macro-/mesoscopic scale studies in biology, radiology, plasma physics to the characterization of 3D atomic structure in material science. The fundamental of…
We construct an image formation theory that covers the majority of optical microscopy techniques that use diverse coherent or incoherent light-matter interactions. The theories of individual microscopy methods could not previously be…
X-ray computed tomography is a powerful tool for volumetric imaging, where three-dimensional (3D) images are generated from a large number of individual X-ray projection images. Collecting the required number of low noise projection images…
The Integral Image algorithm is often applied in tasks that require efficient integration over images, such as object detection. In this paper we discuss theoretical aspects of the algorithm's continuous version. We suggest to define the…
Fourier ptychography has attracted a wide range of focus for its ability of large space-bandwidth-produce, and quantative phase measurement. It is a typical computational imaging technique which refers to optimizing both the imaging…
Optical tomography has emerged as a non-invasive imaging method, providing three-dimensional insights into subcellular structures and thereby enabling a deeper understanding of cellular functions, interactions, and processes. Conventional…
Interior tomography for the region-of-interest (ROI) imaging has advantages of using a small detector and reducing X-ray radiation dose. However, standard analytic reconstruction suffers from severe cupping artifacts due to existence of…